Correct. If you are not incorporate or otherwise organized into an entity.
There is your bank account, too. The income will show on your bank account, so if audited, that will indicate your income.
I would also recommend issuing invoices to the company. Since you will be considered self-employed, you will need to keep substantiation documents.
See if these help:
The Art of Keeping Receipts for Your Taxes
What self-employment expenses can I deduct?
Why am I paying self-employment tax?
Can I deduct health insurance premiums if I am self-employed?
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